Solve for $x$ and $y$ using elimination. ${6x+y = 10}$ ${5x+y = 9}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $-1$ ${-6x-y = -10}$ $5x+y = 9$ Add the top and bottom equations together. $-x = -1$ $\dfrac{-x}{{-1}} = \dfrac{-1}{{-1}}$ ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {6x+y = 10}\thinspace$ to find $y$ ${6}{(1)}{ + y = 10}$ $6+y = 10$ $6{-6} + y = 10{-6}$ ${y = 4}$ You can also plug ${x = 1}$ into $\thinspace {5x+y = 9}\thinspace$ and get the same answer for $y$ : ${5}{(1)}{ + y = 9}$ ${y = 4}$